On Saint-Venant's principle in plane anisotropic elasticity

On Saint-Venant's principle in plane anisotropic elasticity

RI~SUMt~ Par une mdthode applicable ~t un tr~s grand nombre de milieu anisotropique, l'auteur utilise les in6galit6s concern~nt la d~croissance de l'6nergie darts le cas d'un probl~me plan et dans l'hypoth6se de conditions 61astostatiques lin~ahes, l'auteur pr6cise la validit6 du principe de Saint-Venant dans le cadre de ses applications. Une limite in fdrieure (en fonction des constantes 61ast...

Saint-Venant's principle in linear elasticity with microstructure

Toupin's version of the Saint-Venant principle in linear elasticity is generalized to the case of linear elasticity with mierostructure. That is, it is shown that, for a straight prismatic bar made of an isotropic linear elastic material with rnicrostructure and loaded by a self-equilibrated force system at one end only, the strain energy stored in the portion of the bar which is beyond a dista...

On Saint Venant's Principle

The so-called principle of statically equivalent loads, due to Saint Venant, has been referred to for the last fifty years in almost all texts on elasticity. The statements in different books vary only slightly. Let us quote A. E. H. Love's Treatise on the mathematical theory of elasticity (4th éd., p. 132) : "According to this principle the strains that are produced in a body by the applicatio...

An alternative to the Kelvin decomposition for plane anisotropic elasticity

A reciprocity theorem in linear gradient elasticity and the corresponding Saint-Venant principle

In many practical applications of nanotechnology and in microelectromechanical devices, typical structural components are in the form of beams, plates, shells and membranes. When the scale of such components is very small, the material microstructural lengths become important and strain gradient elasticity can provide useful material modelling. In addition, small scale beams and bars can be use...